Acta Futura 4 (2011) 81-97 Acta DOI: 10.2420/AF04.2011.81 Futura Micro-to-Macro: Astrodynamics at Extremes of Length-scale C R. MI,* M C, C C, J-P S R B, J H C L Advanced Space Concepts Laboratory, University of Strathclyde, Glasgow G1 1XJ, United Kingdom Abstract. is paper investigates astrodynamics plied research have translated key ideas from dynami- at extremes of length-scale, ranging from swarms cal astronomy to spacecraft astrodynamics to generate of future ‘smart dust’ devices to the capture and families of orbits which now deliver essential scientific utilisation of small near Earth asteroids. At the and commercial products such as high bandwidth data- smallest length-scales, families of orbits are found links, high resolution multi-spectral imagery and precise which balance the energy gain from solar radiation global positioning. While such exciting space applica- pressure with energy dissipation due to air drag. tions have transformed a range of both commercial and is results in long orbit lifetimes for high area- to-mass ratio ‘smart dust’ devices. High area-to- public services, the continued exploitation of space will mass hybrid spacecraft, using both solar sail and require new innovations both in spacecraft technologies electric propulsion, are then considered to enable and in fundamental astrodynamics. ‘pole-sitter’ orbits providing a polar-stationary van- is paper provides an overview of an on-going pro- tage point for Earth observation. ese spacecraft gramme of work which aims to deliver radically new ap- are also considered to enable displaced geostation- proaches to astrodynamics at extremes of length-scale to ary orbits. Finally, the potential material resource underpin new space-derived products and services for available from captured near Earth asteroids is con- sidered which can underpin future large-scale space space science, telecommunications and Earth observa- engineering ventures. e use of such material for tion. ese include vast swarms of interacting MEMS- geo-engineering is investigated using a cloud of scale ‘smart dust’ devices for new science applications unprocessed dust in the vicinity of the Earth-Sun [9, 23], displaced polar and geostationary orbits for L1 point to fractionally reduce solar insolation. Earth observation and communications [6, 15] and new concepts for the capture and exploitation of small near Earth asteroids [33, 3], as illustrated schematically in 1 Introduction Fig. 1. e growing utilisation of space as a platform for sci- Traditionally, astrodynamics has centred on the classical ence, telecommunications, Earth observation and nav- gravitational two-body problem, with additional forces igation is a direct result of the application of the tools treated as small perturbations. is approach allows the of classical orbital dynamics. Many decades of ap- conic section solutions to the unperturbed gravitational two-body problem to form the basis of an understanding *E-mail address: [email protected] of the weakly perturbed problem (for example [18, 31]). 81 Acta Futura 4 (2011) / 81-97 C.R McInnes et al. a) b) c) F . Micro-to-macro: future space systems at extremes of length-scale (a) MICRO: swarms of ‘smart dust’ sensor nodes (b) MESO: pole-sitter orbits for gossamer spacecraft (c) MACRO: geo-engineering with captured near Earth asteroid material. Such an approach has provided the mathematical tools ing extremely low areal densities. ese spacecraft are to enable, for example, orbit control of geostationary strongly perturbed by atmospheric drag and solar ra- telecommunication satellites, the definition of mapping diation pressure, and in the case of solar sails, utilise orbits for Earth observation satellites and coverage pat- solar radiation pressure directly for propulsion. Sim- terns for satellite navigation constellations. ilarly, micro-spacecraft are rapidly shrinking in mass More recently, the use of modern dynamical systems and volume, driven by advances in integrated micro- 3 theory has led to exciting new developments in the grav- electronics. Since spacecraft mass scales as L , while 2 itational three-body problem (for example [19, 13]). surface area scales as L , effective areal density scales as -1 Work has explored the use of new families of trajectories L with diminishing spacecraft size. is again leads connecting periodic orbits about the collinear libration to strong atmospheric drag and solar radiation pressure points as the basis for highly efficient orbit transfer in perturbations and the possibility of electrodynamic ef- the Earth-Moon and Earth-Sun systems. ese more fects due to natural or artificial surface charging. ere- recent developments are a strong indication that there fore both classes of spacecraft, while at opposing ends is much work still to be done in modern astrodynam- of the length-scale spectrum, will require the integrated ics, and that many new families of useful orbits await development of new methods in astrodynamics to ex- discovery. plore such strongly perturbed orbits. At even larger length-scales, new insights into the three-body problem Future space systems will require a new approach to can enable the capture of small near Earth asteroids by orbital dynamics from micro- to macroscopic length- greatly leveraging the effect of intervention by impulse scales L. is new understanding will be required to or continuous thrust. e ability to efficiently capture underpin the exploitation of future space systems from such material could have a long-term impact on the fea- swarms of interacting MEMS-scale ‘smart dust’ devices sibility and cost of future space systems at the largest ∼ 10-3 (L m) to extremely large gossamer spacecraft length-scales such as space solar power and space-based ∼ 103 (L m). At these extremes of spacecraft length- geo-engineering. scale, perturbations such as atmospheric drag, solar ra- Key questions to be addressed in each of the following diation pressure and electrodynamic forces can be of the three sections include: same order of magnitude as the central two-body or three-body gravitational forces. e strongly perturbed • MICRO: How does the orbital dynamics of micro- nature of the dynamics of such spacecraft gives rise to spacecraft scale with rapidly diminishing space- rich new families of orbits which can be exploited to craft size and how can the orbits of swarms of such deliver new space products and services. devices be controlled? Gossamer spacecraft are characterised by a large deploy- • MESO: Can different natural perturbations and able surface area, but a relatively modest mass, yield- low thrust propulsion technologies be combined to 82 DOI: 10.2420/AF04.2011.81 Micro-to-Macro: Astrodynamics at Extremes of Length-scale enable new families of exploitable orbits for large drag both have a non-negligible effect on the space- gossamer spacecraft? craft orbit, complete equilibrium is not possible. How- ever, the long-term orbit evolution still presents some • MACRO: Can new insights from orbital dynamics intriguing behaviour; if the initial conditions are in a bring forward the development of visionary, large- certain region around the equilibrium solution set, the scale space engineering ventures by efficiently cap- long-term evolution is characterised by librational mo- turing near Earth asteroid resources? tion, progressively decaying due to the non-conservative effect of atmospheric drag [11, 10] (see Fig. 2). It is 2 MICRO: Astrodynamics for smart dust possible to define different arcs of the orbit evolution swarms where the trajectory is dominated either by drag or by solar radiation pressure. 2.1 Long-lived orbits for smart dust devices e natural effects of solar radiation pressure and at- mospheric drag perturbations can be exploited to de- Recent innovations in spacecraft design have exploited sign swarm missions, for example, for the mapping and advances in miniaturisation to fabricate small satellites study of the upper regions of the Earth’s atmosphere with dimensions of a single micro-chip. Low-cost [9]. A swarm of SpaceChips is deployed on the eclip- manufacturing of vast numbers of micro-spacecraft can tic plane from a single spacecraft, as distributed nodes lead to their use in swarm applications, and their small of a network to obtain a spatial and temporal map of dimensions facilitate access-to-space through deploy- the ionosphere and exosphere. By selecting the release ment in orbit as piggy-back on a conventional space- conditions in terms of angular displacement φ between craft. e deployment of vast numbers of ‘SpaceChips’ the orbit pericentre and the direction of the Sun-Earth will enable future missions, such as global sensor net- line, the effect of SRP is exploited to scatter the devices works for Earth observation and communication, dis- into a set of different orbits which cover an extended, tributed space missions for multi-point, real-time sens- but bounded, region of the atmosphere, collecting dis- ing for space science, interplanetary exploration in sup- tributed measurements. port of traditional spacecraft, deployment in the vicin- ity of a spacecraft for environmental and damage de- Figure 2 shows the long-term evolution of the tection, or possibly future space-based geo-engineering SpaceChip swarm after release from a conventional applications. Even if limited, micro-spacecraft are also spacecraft. For the first part of the orbit evolution for capable of long-term orbit control through the exploita- φ < π the secular rate of change of the eccentricity is tion of perturbations such as Lorentz force, solar radia- negative; as a consequence the orbit perigee rises reach- tion pressure or atmospheric drag and vicinity control by ing its maximum at φ = π. Afterwards, when φ > π, means of spacecraft-to-spacecraft interaction through the secular variation of eccentricity is negative, hence the Coulomb force. the perigee height decreases. Moreover, the exploitation of orbital dynamics at ex- Importantly, the short lifetime of high area-to-mass tremely small length-scales can enable novel families of spacecraft can be greatly extended (and indeed selected) exploitable non-Keplerian orbits.